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<a href="_c_v_folds_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">//header needed for cross validation</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="preprocessor">#include &lt;<a class="code" href="_c_v_dataset_tools_8h.html">shark/Data/CVDatasetTools.h</a>&gt;</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span> </div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment">//headers needed for our test problem</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="preprocessor">#include &lt;<a class="code" href="_data_distribution_8h.html">shark/Data/DataDistribution.h</a>&gt;</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="preprocessor">#include &lt;<a class="code" href="_linear_model_8h.html">shark/Models/LinearModel.h</a>&gt;</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="preprocessor">#include &lt;<a class="code" href="_concatenated_model_8h.html">shark/Models/ConcatenatedModel.h</a>&gt;</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="preprocessor">#include &lt;<a class="code" href="_error_function_8h.html">shark/ObjectiveFunctions/ErrorFunction.h</a>&gt;</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="preprocessor">#include &lt;<a class="code" href="_squared_loss_8h.html">shark/ObjectiveFunctions/Loss/SquaredLoss.h</a>&gt;</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="preprocessor">#include &lt;<a class="code" href="_regularizer_8h.html">shark/ObjectiveFunctions/Regularizer.h</a>&gt;</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="preprocessor">#include &lt;<a class="code" href="_rprop_8h.html">shark/Algorithms/GradientDescent/Rprop.h</a>&gt;</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span> </div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment">//we use an artifical learning problem</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="preprocessor">#include &lt;<a class="code" href="_data_distribution_8h.html">shark/Data/DataDistribution.h</a>&gt;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span> </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="keyword">using namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a>;</div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="keyword">using namespace </span>std;</div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"></span> </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment">///In this example, you will learn to create and use partitions</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment">///for cross validation.</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment">///This tutorial describes a handmade solution which does not use the Crossvalidation error function</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment">///which is also provided by shark. We do this, because it gives a better on what Cross Validation does.</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"></span><span class="comment"></span> </div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment">///The Test Problem receives the regularization parameter and a dataset</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment">///and returns the errror. skip to the main if you are not interested</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment">///in the problem itself. But here you can also see how to create</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment">///regularized error functions. so maybe it&#39;s still worth taking a look ;)</span></div>
<div class="foldopen" id="foldopen00028" data-start="{" data-end="}">
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"><a class="line" href="_c_v_folds_8cpp.html#a56b168be2277393c3cb5e6f917fc0831">   28</a></span><span class="comment"></span><span class="keywordtype">double</span> <a class="code hl_function" href="_c_v_folds_8cpp.html#a56b168be2277393c3cb5e6f917fc0831">trainProblem</a>(<span class="keyword">const</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html">RegressionDataset</a>&amp; training, <a class="code hl_class" href="classshark_1_1_labeled_data.html">RegressionDataset</a> <span class="keyword">const</span>&amp; validation, <span class="keywordtype">double</span> regularization){</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    <a class="code hl_class" href="classshark_1_1_linear_model.html" title="Linear Prediction with optional activation function.">LinearModel&lt;RealVector,LogisticNeuron&gt;</a> layer1(1,20);</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    <a class="code hl_class" href="classshark_1_1_linear_model.html" title="Linear Prediction with optional activation function.">LinearModel&lt;RealVector&gt;</a> layer2(20,1);</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    <a class="code hl_class" href="classshark_1_1_concatenated_model.html" title="ConcatenatedModel concatenates two models such that the output of the first model is input to the sec...">ConcatenatedModel&lt;RealVector&gt;</a> network = layer1 &gt;&gt; layer2;</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>    <a class="code hl_function" href="group__shark__globals.html#gaa2a8823f1241e854ba858d79fd3e37a2" title="Initialize model parameters uniformly at random.">initRandomUniform</a>(network,-1,1);</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span> </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    <span class="comment">//the error function is a combination of MSE and 2-norm error</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    <a class="code hl_class" href="classshark_1_1_squared_loss.html" title="squared loss for regression and classification">SquaredLoss&lt;&gt;</a> loss;</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    <a class="code hl_class" href="classshark_1_1_error_function.html" title="Objective function for supervised learning.">ErrorFunction&lt;&gt;</a> error(training,&amp;network,&amp;loss);</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    <a class="code hl_class" href="classshark_1_1_two_norm_regularizer.html" title="Two-norm of the input as an objective function.">TwoNormRegularizer&lt;&gt;</a> regularizer;</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    error.<a class="code hl_function" href="classshark_1_1_error_function.html#af786262cd69579e9b26d28de85b8fde9">setRegularizer</a>(regularization, &amp;regularizer);</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    <span class="comment">//now train for a number of iterations using Rprop</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <a class="code hl_class" href="classshark_1_1_rprop.html" title="This class offers methods for the usage of the Resilient-Backpropagation-algorithm with/out weight-ba...">Rprop&lt;&gt;</a> optimizer;</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>    error.<a class="code hl_function" href="classshark_1_1_error_function.html#a6ba22ddebbfc72a20503c9089e59abe8">init</a>();</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    <span class="comment">//initialize with our predefined point, since</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    <span class="comment">//the combined function can&#39;t propose one.</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    optimizer.<a class="code hl_function" href="classshark_1_1_rprop.html#aa5283be5eb772fcdad29af346c98b498">init</a>(error);</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> iter = 0; iter != 5000; ++iter)</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    {</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>        optimizer.<a class="code hl_function" href="classshark_1_1_rprop.html#a9173edb5b7a84bcd46b62a46445754a6">step</a>(error);</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    }</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <span class="comment">//validate and return the error without regularization</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <span class="keywordflow">return</span> loss(network(validation.<a class="code hl_function" href="group__shark__globals.html#ga6f74e657c7e0c8a32b2456fb328bd653" title="Access to inputs as a separate container.">inputs</a>()),validation.<a class="code hl_function" href="group__shark__globals.html#ga6328a5aa2570c01a5ac5f25076071663" title="Access to labels as a separate container.">labels</a>());</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>}</div>
</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span> </div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span><span class="comment"></span> </div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span><span class="comment">/// What is Cross Validation(CV)? In Cross Validation the dataset is partitioned in</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span><span class="comment">/// several validation data sets. For a given validation dataset the remainder of the dataset</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span><span class="comment">/// - every other validation set - forms the training part. During every evaluation of the error function, </span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span><span class="comment">/// the problem is solved using the training part and the final error is computed using the validation part.</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span><span class="comment">/// The mean of all validation sets trained this way is the final error of the solution found.</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span><span class="comment">/// This quite complex procedure is used to minimize the bias introduced by the dataset itself and makes</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span><span class="comment">/// overfitting of the solution harder.</span></div>
<div class="foldopen" id="foldopen00063" data-start="{" data-end="}">
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"><a class="line" href="_c_v_folds_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">   63</a></span><span class="comment"></span><span class="keywordtype">int</span> <a class="code hl_function" href="_c_v_folds_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>(){</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    <span class="comment">//we first create the problem. in this simple tutorial,</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="comment">//it&#39;s only the 1D wave function sin(x)/x + noise</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <a class="code hl_class" href="classshark_1_1_wave.html" title="Noisy sinc function: y = sin(x) / x + noise.">Wave</a> wave;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <a class="code hl_class" href="classshark_1_1_labeled_data.html">RegressionDataset</a> dataset;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    dataset = wave.<a class="code hl_function" href="classshark_1_1_labeled_data_distribution.html#ace15c1b51c87cd4b553427a55416b155" title="Generates a dataset with samples from from the distribution.">generateDataset</a>(100);</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span> </div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    <span class="comment">//now we want to create the cv folds. For this, we</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <span class="comment">//use the CVDatasetTools.h. There are a few functions</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    <span class="comment">//to create folds. in this case, we create 4</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="comment">//partitions with the same size. so we have 75 train</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    <span class="comment">//and 25 validation data points</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    <a class="code hl_class" href="classshark_1_1_c_v_folds.html">CVFolds&lt;RegressionDataset&gt;</a> folds = <a class="code hl_function" href="group__shark__globals.html#gac5ab39c050dd915797e37fa421db33fd" title="Create a partition for cross validation.">createCVSameSize</a>(dataset,4);</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <span class="comment">//now we want to use the folds to find the best regularization</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    <span class="comment">//parameter for our problem. we use a grid search to accomplish this</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <span class="keywordtype">double</span> bestValidationError = 1e4;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <span class="keywordtype">double</span> bestRegularization = 0;</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <span class="keywordflow">for</span> (<span class="keywordtype">double</span> regularization = 1.e-5; regularization &lt; 1.e-3; regularization *= 2) {</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        <span class="keywordtype">double</span> result = 0;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        <span class="keywordflow">for</span> (std::size_t fold = 0; fold != folds.<a class="code hl_function" href="classshark_1_1_c_v_folds.html#a55e4d73aff1389cb61fc9e41fc1e92ee" title="Returns the number of folds of the dataset.">size</a>(); ++fold){ <span class="comment">//CV</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>            <span class="comment">// access the fold</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>            <a class="code hl_class" href="classshark_1_1_labeled_data.html">RegressionDataset</a> training = folds.<a class="code hl_function" href="classshark_1_1_c_v_folds.html#a71a49586552161e0027348fa3a165310">training</a>(fold);</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>            <a class="code hl_class" href="classshark_1_1_labeled_data.html">RegressionDataset</a> validation = folds.<a class="code hl_function" href="classshark_1_1_c_v_folds.html#a02f53dc5f3585ac17b190bbbe9549b88">validation</a>(fold);</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>            <span class="comment">// train</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>            result += <a class="code hl_function" href="_c_v_folds_8cpp.html#a56b168be2277393c3cb5e6f917fc0831">trainProblem</a>(training, validation, regularization);</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        }</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        result /= folds.<a class="code hl_function" href="classshark_1_1_c_v_folds.html#a55e4d73aff1389cb61fc9e41fc1e92ee" title="Returns the number of folds of the dataset.">size</a>();</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span> </div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        <span class="comment">// check whether this regularization parameter leads to better results</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        <span class="keywordflow">if</span> (result &lt; bestValidationError)</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        {</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            bestValidationError = result;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>            bestRegularization = regularization;</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>        }</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span> </div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        <span class="comment">// print status:</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        std::cout &lt;&lt; regularization &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; result &lt;&lt; std::endl;</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    }</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span> </div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <span class="comment">// print the best value found</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    cout &lt;&lt; <span class="stringliteral">&quot;RESULTS: &quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    cout &lt;&lt; <span class="stringliteral">&quot;======== &quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    cout &lt;&lt; <span class="stringliteral">&quot;best validation error: &quot;</span> &lt;&lt; bestValidationError &lt;&lt; std::endl;</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    cout &lt;&lt; <span class="stringliteral">&quot;best regularization:   &quot;</span> &lt;&lt; bestRegularization&lt;&lt; std::endl;</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>}</div>
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